Systems and methods for real-time well surveillance

ABSTRACT

In an embodiment, a method is performed by a computer system. The method includes integrating a series of data inputs related to a well. The series of data inputs includes at least one real-time data input and at least one non-real-time data input. The method further includes based, at least in part, on a result of the integrating, facilitating a real-time display of performance data for the well. The real-time display includes information related to at least one of hydraulic surveillance and torque-and-drag surveillance.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application claims priority from, and incorporates byreference the entire disclosure of, U.S. Provisional Patent ApplicationNo. 61/873,713, filed on Sep. 4, 2013. This patent application alsoclaims priority from, and incorporates by reference the entiredisclosure of, U.S. Provisional Patent Application No. 61/873,741, filedon Sep. 4, 2013. In addition, this patent application incorporates byreference the entire disclosures of U.S. patent application Ser. Nos.13/829,590, 13/919,240, and 14/018,298.

BACKGROUND

Technical Field

The present disclosure relates generally to drilling analytics and moreparticularly, but not by way of limitation, to systems and methods forreal-time well surveillance.

History of Related Art

An oil well is a general term for any boring through the earth's surfacethat is designed to find petroleum-oil hydrocarbons. An initial life ofan oil well can be viewed in three stages: planning, drilling, andcompletion. During these stages, a huge volume of information isgenerated. This information can be loosely categorized into two types:static data and real-time data. Static data is generated either inadvance (e.g., modeling data, cost predictions, and well plans) or afterevents (e.g., daily reports, mud reports, fracture reports, and casingdata). Static data can be delivered either on a regular basis (e.g.daily reports) or on a per-event basis (e.g., fracture reports andcompletion reports). Real-time data is sensor-derived data that isgenerated through either analysis of fluids (e.g., mud logs) or throughdeploying sensor tools in a well hole. Real-time data can be collectedimmediately via, for example, telemetry, or upon completion of a toolrun (e.g., memory data). Real-time data can be, for example,time-indexed or depth-indexed

During the drilling and completion stages, there has been increasedfocus on remote support and participation. In particular, there issignificant value to be obtained from an ability to analyze in real timevarious data streams that are generated. A typical oil well can requirecollaboration from teams based at the oil well, in regional offices, andcorporate headquarters. This may mean that people thousands of milesapart need to be sure they are looking at the same data sets. These datasets, in turn, may be aggregated from several different streams of data,from historical data generated in previous wells, or from modelspredicted during the planning stage.

Benefits can be gained from cross-correlation and analysis of this data.Historically this has not been possible due to schisms in theorganization of data and the difficulty of sharing many different typesof data in the time constraints required for real-time analysis acrossmultiple locations. Further complications have been generated by therequirement to tightly control access to this data to ensure securityfor what can be extremely valuable information that can have significantmarket impact upon an oil company.

SUMMARY OF THE INVENTION

In an embodiment, a method is performed by a computer system. The methodincludes integrating a series of data inputs related to a well. Theseries of data inputs includes at least one real-time data input and atleast one non-real-time data input. The method further includes based,at least in part, on a result of the integrating, facilitating areal-time display of performance data for the well. The real-timedisplay includes information related to at least one of hydraulicsurveillance and torque-and-drag surveillance.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the method and apparatus of the presentinvention may be obtained by reference to the following DetailedDescription when taken in conjunction with the accompanying Drawingswherein:

FIG. 1 illustrates an example of a system for facilitating real-timewell surveillance; and

FIG. 2 illustrates an example of a computer system;

FIG. 3 illustrates an annular hydraulics workflow;

FIG. 4 illustrates interface inputs for velocity;

FIG. 5 illustrates interface inputs for power law constants;

FIG. 6 illustrates interface inputs for Reynolds Number and criticalReynolds Numbers;

FIG. 7 illustrates an annular hydraulics display;

FIG. 8 illustrates hydraulics at the bit workflow;

FIG. 9 illustrates interface inputs for total flow area;

FIG. 10 illustrates hydraulics at the bit display;

FIG. 11 illustrates a cutting transportation workflow;

FIG. 12 illustrates interface inputs for boundary shear rate;

FIG. 13 illustrates interface inputs for shear stress developed by theparticle;

FIG. 14 illustrates a cutting transportation display;

FIG. 15 illustrates a swab and surge workflow;

FIG. 16 illustrates interface inputs for average maximum speed of pipemovement and equivalent fluid velocity;

FIG. 17 illustrates interface inputs for gel-breaking pressure;

FIG. 18 illustrates a swab and surge display;

FIG. 19 illustrates a technical workflow;

FIG. 20 illustrates movement of variables through a system and theinterdependency of subsystems;

FIG. 21 illustrates a diagram to explain the numbering of bottom holeassembly (BHA) sections;

FIG. 22 illustrates a diagram to show the number assigned to eachactivity;

FIG. 23 illustrates a diagram to show the numbers assigned to eachwellbore condition;

FIG. 24 shows an example of a real-time display console that can providefor Torque and Drag analysis;

FIG. 25 shows an alternative display with the broomstick graphsdisplayed horizontally;

FIG. 26 illustrates an example of the hookload and friction factordisplay;

FIG. 27 shows a display that combines that graphs from the Torque & DragDisplay and the graphs from the Hookload and Friction Factor Display;

FIG. 28 illustrates a display according to an embodiment of the presentdisclosure;

FIG. 29 illustrates a display according to an embodiment of the presentdisclosure;

FIG. 30 illustrates a display according to an embodiment of the presentdisclosure; and

FIG. 31 illustrates a display according to an embodiment of the presentdisclosure.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS OF THE INVENTION

FIG. 1 illustrates an example of a system 100 for facilitating real-timewell surveillance. The system 100 includes a wellsite computer system102, a central computing system 108, and a communications network 106.The wellsite computer system 102 includes a collection server 120, aremote-integration server 122, and a network link 124. The centralcomputing system 108 includes a main server 110, a repository server112, and a network link 126. It should be appreciated that the depictedconfigurations of the central computing system 108 and the wellsitecomputer system 102 are illustrative in nature. The central computingsystem 108 and the wellsite computer system can each include any numberof physical or virtual server computers and databases. For example, invarious embodiments, the remote-integration server 122 may be omitted orhave its functionality integrated into the collection server 120. Othermodifications and rearrangements will be apparent to one of ordinaryskill in the art after reviewing inventive principles contained herein.

In a typical embodiment, the wellsite computer system 102 is located ator near a wellsite for a current well and communicates with the centralcomputing system 108 over the communications network 106. Thecommunications network 106 may include, for example, satellitecommunication between the network link 124 of the wellsite computersystem 102 and the network link 126 of the central computing system 108.Thus, the network link 124 and the network link 126 can be, for example,satellite links. For simplicity of description, communication betweenthe wellsite computer system 102 and the central computing system 108may be described below without specific reference to the network link124, the network link 126, and the communications network 106.

Using, for example, logging while drilling (LWD), the collection server120 receives and/or generates channel data 104 (e.g., in WITS0) via datareceived from sensors that are in use at the wellsite. A given sensor orother source of data is referred to herein as a “channel.” Data from achannel may be referred to as “channel data,” which term is inclusive ofboth raw data and metadata. The raw data includes, for example, measureddata determined by the sensor or source. The measured data can include,for example, resistivity, porosity, permeability, density, and gamma-raydata. The metadata includes information about the raw data such as, forexample, time, depth, identification information for the channel, andthe like. The collection server 120 transmits the channel data 104 tothe remote-integration server 122, which communicates the channel data104 to the central computing system 108 in real-time.

On the central computing system 108, the main server 110 receives thechannel data 104 from the wellsite computer system 102 and converts thechannel data 104 to a common data format. The conversion of channel datato a common data format is described in detail in U.S. patentapplication Ser. No. 13/829,590, which application is incorporated byreference above. As shown, the main server 110 has a calculation engine128 resident thereon. Via the calculation engine 128, the main server110 generates calculated data in real-time based on the channel data104. The calculation engine 128 can be, for example, a softwareapplication that implements algorithms to generate the calculated data.The calculation engine 128 can also maintain settings that are utilizedfor generating the calculated data.

The repository server 112 stores and maintains the channel data 104 andany calculated data according to the common data format. Storage andmaintenance of data according to the common data format is described indetail in U.S. patent application Ser. No. 13/829,590, which applicationis incorporated by reference above. In a typical embodiment, therepository server 112 stores channel data from a plurality of wellsitecomputer systems located at a plurality of wellsites in this fashion.

The repository server 112 facilitates a real-time display 114 ofdrilling-performance data (e.g., information related to hydraulicsurveillance, torque-and-drag surveillance, etc.) related to thewellsite. In a typical embodiment, the real-time display 114 is providedvia a network such as, for example, the Internet, via a web interface.In some cases, the real-time display 114 can be shown and updated inreal time on a computing device 116 as the channel data 104 is received.In a typical embodiment, the real-time display 114 allows engineeringpersonnel 118 to perform real-time analysis for the wellsite.

FIG. 2 illustrates an example of a computer system 200. In variouscases, the computer system 200 can be generally representative, forexample, of the wellsite computer system 102 and/or the centralcomputing system 108. In addition, or alternatively, the computer system200 can be an example of the collection server 120, theremote-integration server 122, the main server 110, the repositoryserver 112, and/or the like.

The computer system 200 may itself include one or more portions of oneor more computer systems. In particular embodiments, one or more ofthese computer systems may perform one or more steps of one or moremethods described or illustrated herein and/or incorporated by referenceherein. In particular embodiments, one or more computer systems mayprovide functionality described or illustrated herein. In particularembodiments, encoded software running on one or more computer systemsmay perform one or more steps of one or more methods described orillustrated herein or provide functionality described or illustratedherein.

The components of the computer system 200 may comprise any suitablephysical form, configuration, number, type and/or layout. As an example,and not by way of limitation, the computer system 200 may comprise anembedded computer system, a system-on-chip (SOC), a single-boardcomputer system (SBC) (such as, for example, a computer-on-module (COM)or system-on-module (SOM)), a desktop computer system, a laptop ornotebook computer system, an interactive kiosk, a mainframe, a mesh ofcomputer systems, a mobile telephone, a personal digital assistant(PDA), a server, or a combination of two or more of these. Whereappropriate, the computer system 200 may include one or more computersystems; be unitary or distributed; span multiple locations; spanmultiple machines; or reside in a cloud, which may include one or morecloud components in one or more networks.

In the depicted embodiment, the computer system 200 includes a processor211; memory 213; storage 215; interface 217; and bus 219. Although aparticular computer system is depicted having a particular number ofparticular components in a particular arrangement, this disclosurecontemplates any suitable computer system 200 having any suitable numberof any suitable components in any suitable arrangement.

Processor 211 may be a microprocessor, controller, or any other suitablecomputing device, resource, or combination of hardware, software and/orencoded logic operable to provide, either alone or in conjunction withother components, (e.g., memory 213) wireless networking functionality.Such functionality may include providing various features discussedherein. For example, processor 211 may facilitate one or moreapplications that provide real-time surveillance as described herein. Inparticular embodiments, processor 211 may include hardware for executinginstructions, such as those making up a computer program. As an exampleand not by way of limitation, to execute instructions, processor 211 mayretrieve (or fetch) instructions from an internal register, an internalcache, memory 213, or storage 215; decode and execute them; and thenwrite one or more results to an internal register, an internal cache,memory 213, or storage 215.

In particular embodiments, processor 211 may include one or moreinternal caches for data, instructions, or addresses. This disclosurecontemplates processor 211 including any suitable number of any suitableinternal caches, where appropriate. As an example and not by way oflimitation, processor 211 may include one or more instruction caches,one or more data caches, and one or more translation lookaside buffers(TLBs). Instructions in the instruction caches may be copies ofinstructions in memory 213 or storage 215 and the instruction caches mayspeed up retrieval of those instructions by processor 211. Data in thedata caches may be copies of data in memory 213 or storage 215 forinstructions executing at processor 211 to operate on; the results ofprevious instructions executed at processor 211 for access by subsequentinstructions executing at processor 211, or for writing to memory 213,or storage 215; or other suitable data. The data caches may speed upread or write operations by processor 211. The TLBs may speed upvirtual-address translations for processor 211. In particularembodiments, processor 211 may include one or more internal registersfor data, instructions, or addresses. Depending on the embodiment,processor 211 may include any suitable number of any suitable internalregisters, where appropriate. Where appropriate, processor 211 mayinclude one or more arithmetic logic units (ALUs); be a multi-coreprocessor; include one or more processors 211; or any other suitableprocessor.

Memory 213 may be any form of volatile or non-volatile memory including,without limitation, magnetic media, optical media, random access memory(RAM), read-only memory (ROM), flash memory, removable media, or anyother suitable local or remote memory component or components. Inparticular embodiments, memory 213 may include random access memory(RAM). This RAM may be volatile memory, where appropriate. Whereappropriate, this RAM may be dynamic RAM (DRAM) or static RAM (SRAM).Moreover, where appropriate, this RAM may be single-ported ormulti-ported RAM, or any other suitable type of RAM or memory. Memory213 may include one or more memories 213, where appropriate. Memory 213may store any suitable data or information utilized by computer system200, including software embedded in a computer readable medium, and/orencoded logic incorporated in hardware or otherwise stored (e.g.,firmware). In particular embodiments, memory 213 may include main memoryfor storing instructions for processor 211 to execute or data forprocessor 211 to operate on. In particular embodiments, one or morememory management units (MMUs) may reside between processor 211 andmemory 213 and facilitate accesses to memory 213 requested by processor211.

As an example and not by way of limitation, computer system 200 may loadinstructions from storage 215 or another source (such as, for example,another computer system) to memory 213. Processor 211 may then load theinstructions from memory 213 to an internal register or internal cache.To execute the instructions, processor 211 may retrieve the instructionsfrom the internal register or internal cache and decode them. During orafter execution of the instructions, processor 211 may write one or moreresults (which may be intermediate or final results) to the internalregister or internal cache. Processor 211 may then write one or more ofthose results to memory 213. In particular embodiments, processor 211may execute only instructions in one or more internal registers orinternal caches or in memory 213 (as opposed to storage 215 orelsewhere) and may operate only on data in one or more internalregisters or internal caches or in memory 213 (as opposed to storage 215or elsewhere).

In particular embodiments, storage 215 may include mass storage for dataor instructions. As an example and not by way of limitation, storage 215may include a hard disk drive (HDD), a floppy disk drive, flash memory,an optical disc, a magneto-optical disc, magnetic tape, or a UniversalSerial Bus (USB) drive or a combination of two or more of these. Storage215 may include removable or non-removable (or fixed) media, whereappropriate. Storage 215 may be internal or external to computer system200, where appropriate. In particular embodiments, storage 215 may benon-volatile, solid-state memory. In particular embodiments, storage 215may include read-only memory (ROM). Where appropriate, this ROM may bemask-programmed ROM, programmable ROM (PROM), erasable PROM (EPROM),electrically erasable PROM (EEPROM), electrically alterable ROM (EAROM),or flash memory or a combination of two or more of these. Storage 215may take any suitable physical form and may comprise any suitable numberor type of storage. Storage 215 may include one or more storage controlunits facilitating communication between processor 211 and storage 215,where appropriate.

In particular embodiments, interface 217 may include hardware, encodedsoftware, or both providing one or more interfaces for communication(such as, for example, packet-based communication) among the wellsitecomputer system 102, the central computing system 108, any networks, anynetwork devices, and/or any other computer systems. As an example andnot by way of limitation, communication interface 217 may include anetwork interface controller (NIC) or network adapter for communicatingwith an Ethernet or other wire-based network and/or a wireless NIC(WNIC) or wireless adapter for communicating with a wireless network.

In some embodiments, interface 217 comprises one or more radios coupledto one or more physical antenna ports 116. Depending on the embodiment,interface 217 may be any type of interface suitable for any type ofnetwork for which computer system 200 is used. As an example and not byway of limitation, computer system 200 can include (or communicate with)an ad-hoc network, a personal area network (PAN), a local area network(LAN), a wide area network (WAN), a metropolitan area network (MAN), orone or more portions of the Internet or a combination of two or more ofthese. One or more portions of one or more of these networks may bewired or wireless. As an example, computer system 200 can include (orcommunicate with) a wireless PAN (WPAN) (such as, for example, aBLUETOOTH WPAN), a WI-FI network, a WI-MAX network, an LTE network, anLTE-A network, a cellular telephone network (such as, for example, aGlobal System for Mobile Communications (GSM) network), or any othersuitable wireless network or a combination of two or more of these.Computer system 200 may include any suitable interface 217 for any oneor more of these networks, where appropriate.

In some embodiments, interface 217 may include one or more interfacesfor one or more I/O devices. One or more of these I/O devices may enablecommunication between a person and computer system 200. As an exampleand not by way of limitation, an I/O device may include a keyboard,keypad, microphone, monitor, mouse, printer, scanner, speaker, stillcamera, stylus, tablet, touchscreen, trackball, video camera, anothersuitable I/O device or a combination of two or more of these. An I/Odevice may include one or more sensors. Particular embodiments mayinclude any suitable type and/or number of I/O devices and any suitabletype and/or number of interfaces 217 for them. Where appropriate,interface 217 may include one or more drivers enabling processor 211 todrive one or more of these I/O devices. Interface 217 may include one ormore interfaces 217, where appropriate.

Bus 219 may include any combination of hardware, software embedded in acomputer readable medium, and/or encoded logic incorporated in hardwareor otherwise stored (e.g., firmware) to couple components of computersystem 200 to each other. As an example and not by way of limitation,bus 219 may include an Accelerated Graphics Port (AGP) or other graphicsbus, an Enhanced Industry Standard Architecture (EISA) bus, a front-sidebus (FSB), a HYPERTRANSPORT (HT) interconnect, an Industry StandardArchitecture (ISA) bus, an INFINIBAND interconnect, a low-pin-count(LPC) bus, a memory bus, a Micro Channel Architecture (MCA) bus, aPeripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus,a serial advanced technology attachment (SATA) bus, a Video ElectronicsStandards Association local (VLB) bus, or any other suitable bus or acombination of two or more of these. Bus 219 may include any number,type, and/or configuration of buses 219, where appropriate. Inparticular embodiments, one or more buses 219 (which may each include anaddress bus and a data bus) may couple processor 211 to memory 213. Bus219 may include one or more memory buses.

Herein, reference to a computer-readable storage medium encompasses oneor more tangible computer-readable storage media possessing structures.As an example and not by way of limitation, a computer-readable storagemedium may include a semiconductor-based or other integrated circuit(IC) (such, as for example, a field-programmable gate array (FPGA) or anapplication-specific IC (ASIC)), a hard disk, an HDD, a hybrid harddrive (HHD), an optical disc, an optical disc drive (ODD), amagneto-optical disc, a magneto-optical drive, a floppy disk, a floppydisk drive (FDD), magnetic tape, a holographic storage medium, asolid-state drive (SSD), a RAM-drive, a SECURE DIGITAL card, a SECUREDIGITAL drive, a flash memory card, a flash memory drive, or any othersuitable tangible computer-readable storage medium or a combination oftwo or more of these, where appropriate.

Particular embodiments may include one or more computer-readable storagemedia implementing any suitable storage. In particular embodiments, acomputer-readable storage medium implements one or more portions ofprocessor 211 (such as, for example, one or more internal registers orcaches), one or more portions of memory 213, one or more portions ofstorage 215, or a combination of these, where appropriate. In particularembodiments, a computer-readable storage medium implements RAM or ROM.In particular embodiments, a computer-readable storage medium implementsvolatile or persistent memory. In particular embodiments, one or morecomputer-readable storage media embody encoded software.

Herein, reference to encoded software may encompass one or moreapplications, bytecode, one or more computer programs, one or moreexecutables, one or more instructions, logic, machine code, one or morescripts, or source code, and vice versa, where appropriate, that havebeen stored or encoded in a computer-readable storage medium. Inparticular embodiments, encoded software includes one or moreapplication programming interfaces (APIs) stored or encoded in acomputer-readable storage medium. Particular embodiments may use anysuitable encoded software written or otherwise expressed in any suitableprogramming language or combination of programming languages stored orencoded in any suitable type or number of computer-readable storagemedia. In particular embodiments, encoded software may be expressed assource code or object code. In particular embodiments, encoded softwareis expressed in a higher-level programming language, such as, forexample, C, Perl, or a suitable extension thereof. In particularembodiments, encoded software is expressed in a lower-level programminglanguage, such as assembly language (or machine code). In particularembodiments, encoded software is expressed in JAVA. In particularembodiments, encoded software is expressed in Hyper Text Markup Language(HTML), Extensible Markup Language (XML), or other suitable markuplanguage.

For purposes of illustration, examples of performing real-time wellsurveillance are described in U.S. Provisional Patent Application Nos.61/873,713 and 61/873,741, which applications are incorporated byreference above. In certain embodiments, the described examples canleverage one or more of the computer systems described above withrespect to FIGS. 1-2.

HYDRAULIC SURVEILLANCE IN ANALYSIS REAL-TIME

The hydraulic surveillance analysis in real time takes a series ofreal-time and non-real-time inputs while combining and integratingseveral workflows to reduce a unique engineering real-time suite full ofoutputs and graphs. The hydraulic analyses following the drill stringdesign for drill pipes, drill collar, among annular spaces as well,taking in consideration the boundaries to get the hole clean and savetime as possible. The hydraulic suite in real-time has addressed morethan 98 different hydraulic analyses to get the most complete hydraulicanalysis ever made in real-time.

Several companies have individual worksheets or calculators to computevalues manually, but these results only represent an instant in time anddepth, whereas real-time values are for all instants of time and depthover the duration of the program run. This will benefit companies bygiving real-time feedback about drilling performance, allowing immediateaction to prevent drilling hazards that would otherwise lead tocatastrophic problems, such as, stuck pipe, blowouts, and more.

Advantages are as follows: (1) provide a full analysis in real-time fordrill pipe, drill collars, and annular spaces on the well throughoutvelocities, effectives viscosities, pressure losses, equivalentcirculation density, shear stresses, transport velocities, transportefficiencies—hole cleaning, cutting transportations—hole cleaning, losspressure at the bit, hydraulic power and impact force among swab andsurge analyses; (2) help to prevent blowouts because the system canmeasure the delta of the SSP real versus plan, considering the featuresof the well in real-time; (3) save millions of US dollars because of thesupport that the system can provide within the decision making process;(4) improve the health condition of the well because the results arebeing updated in real-time, including non-real values, such as Lecture300, Lecture 600, L3, and L6, to analyze the mud properties on thebottom of the well; and (5) represent an economic solution which avoidsthe use of expensive tools such as pressure while drilling (PWD) tomeasure the annular pressure on the well.

Each equation setout below will have a definition of what the equationsrepresent, notes, and interface requirements. Table 1 below illustratesunit abbreviations.

TABLE 1 Unit Abbreviation inch in centimeter cm foot ft meter m gallongal liter L pound (mass) lb pound (force) lbF kilogram kg newton Nsecond s minute min hour hr pounds per square inch psi pascal Pacentipoise cP horse power hp watt W percent % decimal dec

INPUTS

The following list contains inputs that will process the output for theoverall hydraulics real-time analysis. The name of every input is given,along with its respective symbol, its units, and whether the data iscollected in real-time (RT), or not in real-time (NRT), Table 2 belowillustrates list of inputs.

TABLE 2 # Name Symbol Units RT/NRT 1 Bit Outside Diameter d_(h) in ft cm— NRT 2 Casing Inside Diameter d_(c) in ft cm — NRT 3 Drill Pipe InsideDiameter d_(dpi) in ft cm — NRT 4 Drill Pipe Outside d_(dpo) in ft cm —NRT Diameter 5 Drill Collar Inside ddci in ft cm — NRT Diameter 6 DrillCollar Outside ddco in ft cm — NRT Diameter 7 Volumetric Flow Rate Qgal/min ft³/min L/min m³/min RT 8 Lecture, 600 RPM θ₀₆₀₀ n/a — — — NRT 9Lecture, 300 RPM θ₀₃₀₀ n/a — — — NRT 10 Lecture, 3 RPM θ₃ n/a — — — NRT11 Mud Weight ρ lb/gal lb/ft³ kg/L kg/m³ RT 12 Measured Depth D_(md) ftm — — RT 13 True Vertical Depth D_(tvd) ft m — — RT 14 Drill Pipe LengthL_(dp) ft m — — NRT 15 Drill Collars Length L_(dc) ft m — — NRT 16 LastCasing Length Lc ft in — — NRT 17 Jet Diameter J in/32 cm — — NRT 18Average Particle Diameter d_(cut) in cm — — NRT 19 Average Particle T incm — — NRT Thickness 20 Rate of Penetration ROP ft/hr m/hr — — RT 21Time From Slips to Slips t s min — — NRT 22 Stand Length L_(s) ft m — —NRT 23 Current Bit Depth D_(bc) ft m — — RT 24 Previous Bit Depth D_(bp)ft m — — RT 25 30-Minute Gel Strength τ₃₀ lbF/100 ft² N/m² — — NRT

SUMMARY OF OUTPUTS

Table 3 below breaks down all of the output data that is found in thesections that follow. The number field represents the equation number.If the units for a particular output are listed as “n/a” then the outputis dimensionless. Many of these outputs will be used in equations asinputs; they are listed here, instead of the input list, to separateuser inputs from equation outputs used as inputs. Also, the symbolslisted are generic. In practical use, they will have subscriptsdescribing the location (such as “dp” for drill pipe or “dch” for theannulus between the drill collar and open hole). Table 3 belowillustrates list of outputs.

TABLE 3 Eq. # Name Symbol Units 1, 2 Velocity v ft/min m/min — — 3, 5Power Law Constant n n n/a — — — 4, 6 Power Law Constant k k P Reyn — —7, 8, 45 Effective Viscosity μ cP Reyn — — 9, 10, 46 Reynolds Number Ren/a — — — 11, 12, 47, Critical Reynolds Number Re_(max) n/a — — — 48 13Critical Annular Velocity v_(crit) ft/min m/min — — 14 Critical Annularlow Rate Q_(crit) gal/min ft³/min L/min m³/min 15-20, 49- FanningFriction Factor f n/a — — — 10 21, 22, 52 Pressure Loss Gradient Δ(p/L)psi/ft ppg/ft Pa/m — 23-27, 53- Pressure Loss Due to Friction Δp psi ppgPa — 55 28 Equivalent Circulating Density ECD lb/gal lb/ft³ kg/L kg/m³29 Total Flow Area A in² ft² cm² — 30 Jet Velocity v_(jet) ft/min m/min.— — 31 Lost Pressure at the Bit Δp_(b) psi ppg Pa — 32 Hydraulic Power Php W — — 33 Hydraulic Power per Unit Area P_(A) hp/in² W/cm² — — 34Impact Force F_(i) lbF N — — 35 Boundary Shear Rate γ_(b) s⁻¹ min⁻¹ — —36 Shear Stress Developed by the τ_(p) lbF/100 ft² N/m² — — Particle 37Shear Rate Developed by the Particle γ_(p) s⁻¹ min⁻¹ — — 38, 39 SlipVelocity v_(s) ft/min m/min — — 40 Transport Velocity v_(t) ft/min m/min— — 41 Transport Efficiency E_(t) % dec — — 42 Cuttings Concentration C% dec — — 43 Average Maximum Speed of Pipe v_(p) ft/min m/min — —Movement 44 Equivalent Fluid Velocity v_(e) ft/min m/min — — 56, 57Equivalent Mud Weight σ_(e) lb/gal lb/ft³ kg/L kg/m³ 58 Gel-BreakingPressure p_(g) psi ppg Pa —

CONVERSION FACTORS

There will be one equation for each output, meaning there can be one setof units used to calculate the output. Therefore, the calculation enginehas a series of conversion factors preprogrammed to convert units intothose used by the equation. Table 4 and Table 5 below show thesefactors. The term “CF” as it is used in the next two tables (Table 4 andTable 5) stands for “Conversion Factor.” Table 4 below illustrates inputunit conversion factors.

TABLE 4 Alt. Alt. Equation Alt. Unit 1 CF1 Unit 2 CF2 Unit 3 CF3 InputUnit ft 12 cm 0.3937 — — in cm 12.598 — — — — in/32 m 3.2808 — — — — ftmin 60 — — — — s ft³/min 7.4805 L/min 0.1198 m³/min 199.83 gal/minlb/ft³ 0.1337 kg/L 3.7854 kg/m³ 0.0038 lb/gal m/hr 3.2808 — — — — ft/hrN/m2 2.0885 — — — — lbF/100f²

There is a list of output conversions to display the output in the unitspreferred by the operator. The following table has this list. Table 5below illustrates output unit conversion factors.

TABLE 5 Equation Alt. Alt. Alt. Output Unit Unit Unit Unit 1 CF1 2 CF2 3CF3 ft/min m/min 0.3048 — — — — P Reyn 1.45E−05 — — — — cP Reyn 1.45E−07— — — — gal/min ft³/min 0.1337 L/min 3.7854 m³/min 0.0038 psi/ft ppg/ft19.25 Pa/m 22621 — — psi ppg 19.25 Pa 6894.8 — — lb/gal lb/ft³ 7.4805kg/L 0.1198 kg/m 119.83 in² cm² 6.4516 — — — — hp W 745.7 — — — — hp/in²W/cm² 115.584 — — — — lbF N 4.448 — — — — s⁻¹ min⁻¹ 60 — — — — % dec0.01 — — — —

The conversion goes from the unit on the left (alternate unit on Table4; equation output unit on Table 5) to the unit on the right (equationinput unit on Table 4; alternate unit on Table 5) using the conversionfactor listed to the right of the alternate unit being utilized.

ANNULAR HYDRAULICS

FIG. 3 illustrates an annular hydraulics workflow. Inside each of theprocess boxes of the flowchart, there are two numbers. The number on theleft represents the total number of outputs that are in real-time. Thereare 15 total inputs (2 RT) in this section that produce 50 total outputs(36 RT)

1. Velocity

Velocity refers to the rate by which the fluid changes position overtime. This is a component in maintaining drilling operations. If thevelocity is too low within the annulus (the region between the drillstring and hold or casing), cuttings will not be lifted away from thebit, possibly leading to stuck pipe, and if the velocity is too high,the drilling fluid will become turbulent and could cause erosion of theformation.

Equation 1 below illustrates velocity inside the drill pipe and drillcollar.

$\begin{matrix}{v = \frac{24.51\; Q}{d^{2}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$where, d: drill pipe inside diameter OR drill collar inside diameter.

Equation 2 below illustrates velocity inside the annulus.

$\begin{matrix}{v = \frac{24.51\; Q}{d_{2}^{2} - d_{1}^{2}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$where, OPEN HOLE:

d₁—drill pipe outside diameter OR drill collar outside diameter

d₂—drill bit outside diameter; and

where, CASED HOLE:

d₁—drill pipe outside diameter

d₂—casing diameter.

Notes: Inputs: diameters are measured in (in) and flow rates is measuredin

$( \frac{gal}{\min} ).$Output: velocity is measured in

$( \frac{ft}{\min} ).$

For more information on input and output values, please refer to theTable 2 and Table 3, respectively.

Interface Requirements: The diameters of the drill pipe, drill collar,casing, and bit (hole) change at certain depths in the drilling process.Therefore, the interface needs inputs for the depths at which thediameters will change and what the new ones will be. Then, calculationswill be run for all active sections of pipe, collar, and casing. SeeFIG. 4 illustrating interface inputs for velocity.

2. Power Law Constants

The Power Law describes the behavior of the non-Newtonian fluids interms of effective viscosity. The ‘n’ constant defines the degree ofshear thinning. A low ‘n’ means that the mud will become less viscouswith increasing shear stress, and vice versa. The ‘k’ constant definesthe viscosity of the mud at a shear stress of 1 s⁻¹.

Equation 3 below illustrates the ‘n’ constant in the string.

$\begin{matrix}{n_{s} = {3.32\;{\log_{10}( \frac{\theta_{600}}{\theta_{300}} )}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

Equation 4 below illustrates the ‘k’ constant in the string.

$\begin{matrix}{k_{s} = \frac{5.11\;\theta_{600}}{1022^{n_{s}}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

Equation 5 below illustrates the ‘n’ constant in the annulus.

$\begin{matrix}{n_{a} = {0.5\;{\log_{10}( \frac{\theta_{300}}{\theta_{3}} )}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

Equation 6 below illustrates the ‘k’ constant in the annulus.

$\begin{matrix}{k_{a} = \frac{5.11\;\theta_{300}}{511^{n_{a}}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

Notes: Inputs 0₆₀₀, 0₃₀₀, and 0₃ are values that come from the mudreport. They are (dimensionless). Outputs: ‘n’ values are(dimensionless). ‘k’ values are measured in (P). These values are notcalculated in real-time. For more information on input and outputvalues, please refer to the Table 2 and Table 3, respectively.

Interface Requirements: In order to calculate the power law constants(‘n’ and ‘k’), the interface has a place to connect a link to the dailymud report in order to obtain the lecture values. See FIG. 5illustrating interface inputs for power law constants.

3. Effective Viscosity

Viscosity cannot be calculated normally for non-Newtonian fluids. As aresult, calculations are preformed to determine the effective viscosity(a comparable value for use in equations).

Equation 7 below illustrates effective viscosity inside the drill pipeand drill collar.

$\begin{matrix}{\mu = {100\;{k_{s}( \frac{96\; v}{60\; d} )}^{n_{s} - 1}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$where, d: drill pipe inside diameter OR drill collar inside diameter.

Equation 8 below illustrates effective viscosity inside the annulus.

$\begin{matrix}{\mu = {100\;{k_{a}\lbrack \frac{144\; v}{60( {d_{2} - d_{1}} )} \rbrack}^{n_{a} - 1}}} & {{Equation}\mspace{14mu} 8}\end{matrix}$where, OPEN HOLE:

d₁—drill pipe outside diameter OR drill collar outside diameter

d₂—drill bit outside diameter; and

where, CASED HOLE:

d₁—drill pipe outside diameter

d₂—casing diameter.

Notes: Inputs: diameters are measure in (in) and velocity in measure in

$( \frac{ft}{\min} ).$Output: viscosity is measured in (cP). For more information on input andoutput values, please refer to the Table 2 and Table 3, respectively.

Interface Requirements: No additional interface requirements.

4. Reynolds Number and Critical Reynolds Numbers

The Reynolds number represents the ratio between the inertial andviscous forces. High Reynolds numbers represent more erratic flow withinthe turbulent regime. Lower numbers represent smoother flow within thelaminar regime. The critical Reynolds numbers represent the boundariesbetween laminar, transitional, and turbulent flow within the string andannulus.

Equation 9 below illustrates Reynolds number inside the drill pipe anddrill collar.

$\begin{matrix}{{Re} = \frac{928{v \cdot d \cdot \rho}}{60\;{\mu( \frac{{3\; n_{s}} + 1}{4\; n_{s}} )}^{n_{s}}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$where, d: drill pipe inside diameter OR drill collar inside diameter.

Equation 10 below illustrates Reynolds number inside the annulus.

$\begin{matrix}{{Re} = \frac{928{v( {d_{2} - d_{1}} )}\rho}{60\;{\mu( \frac{{2\; n_{a}} + 1}{3n_{a}} )}^{n_{a}}}} & {{Equation}\mspace{14mu} 10}\end{matrix}$where, OPEN HOLE:

d₁—drill pipe outside diameter OR drill collar outside diameter

d₂—drill bit outside diameter; and

where, CASED HOLE:

d₁—drill pipe outside diameter

d₂—casing diameter.

Equation 11 below illustrates minimum critical Reynolds number.

$\begin{matrix}{{Re}_{m\; i\; n} = {3470 - {1370\; n}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

Equation 12 below illustrates maximum critical Reynolds Number.

$\begin{matrix}{{Re}_{m\; a\; x} = {4270 - {1370\; n}}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

Notes: Inputs: diameters are measured in (in), velocity is measured in

$( \frac{ft}{\min} ),$mud weight is measured in

$( \frac{lb}{gal} )$viscosity is measured in (cP), and the flow behavior index is(dimensionless). Output: Reynolds number is (dimensionless). For moreinformation on input and output values, please refer to the Table 2 andTable 3, respectively. If the Reynolds number calculated in the previoussection is: (a) below the minimum critical value, the flow is laminar;(b) between the minimum and maximum, the flow is transitional; and (c)above the maximum, the flow is turbulent.

Interface Requirements: In order to calculate the Reynolds Numbers, theinterface has a location to input mud weight values. Also, since theformations are different at different depths, the mud weights vary bydepth, meaning the interface accounts for this as well. See FIG. 6illustrating interface inputs for Reynolds number and critical Reynoldsnumbers.

5. Annular Critical Values

The annular critical velocity and annular critical flow rate values arelimits within which laminar flow exists.

Equation 13 below illustrates annular critical velocity.

$\begin{matrix}{v_{crit} = {60\lbrack \frac{100\;{{Re}_{a_{m\; i\; n}} \cdot {k_{a}( \frac{{2\; n_{a}} + 1}{3\; n_{a}} )}^{n_{a}}}}{928\;{\rho( {d_{2} - d_{1}} )}( \frac{144}{d_{2} - d_{1}} )^{1 - n_{a}}} \rbrack}^{\frac{1}{2 - n_{a}}}} & {{Equation}\mspace{14mu} 13}\end{matrix}$where, OPEN HOLE:

d₁—drill pipe outside diameter OR drill collar outside diameter

d₂—drill bit outside diameter; and

where, CASED HOLE:

d₁—drill pipe outside diameter

d₂—casing diameter.

Equation 14 below illustrates annular critical flow rate.

$\begin{matrix}{Q_{crit} = \frac{2.45\;{v_{crit}( {d_{2}^{2} - d_{1}^{2}} )}}{60}} & {{Equation}\mspace{14mu} 14}\end{matrix}$where, OPEN HOLE:

d₁—drill pipe outside diameter OR drill collar outside diameter

d₂—drill bit outside diameter; and

where, CASED HOLE:

d₁—drill pipe outside diameter

d₂—casing diameter.

Notes: Inputs: diameters are measured in (in), n values are(dimensionless, k values are measured in (P), Reynolds numbers are(dimensionless), mud weight is measured in

$( \frac{lb}{gal} ).$and velocity is measured in

$( \frac{ft}{\min} ).$Outputs: velocity is measured in

$( \frac{ft}{\min} )$and annular flow rate is measured in

$( \frac{gal}{\min} ).$For more information on input and output values, please refer to theTable 2 and Table 3, respectively.

Interface Requirements: No additional interface requirements.

6. Fanning Friction Factor

The fanning friction factor relates the pressure loss due to friction tothe average velocity of fluid flow. This is essentially the same as afriction coefficient for two materials sliding across each other.

Equation 15 below illustrates fanning friction inside the drill pipe anddrill collar for laminar flow.

$\begin{matrix}{f = \frac{16}{Re}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

Equation 16 below illustrates fanning friction factor inside the annulusfor laminar flow.

$\begin{matrix}{f = \frac{24}{Re}} & {{Equation}\mspace{14mu} 16}\end{matrix}$

Equation 17 below illustrates fanning friction factor inside the drillpipe and drill collar for transitional flow.

$\begin{matrix}{f = {{( \frac{{Re} - {Re}_{s_{m\; i\; n}}}{800} )( {\frac{{\log_{10}\lbrack n_{s} \rbrack} + 3.93}{50\;{{Re}_{s_{\max}}}^{\lbrack\frac{1.75 - {\log_{10}{(n_{s})}}}{7}\rbrack}} - \frac{16}{{Re}_{s_{m\; i\; n}}}} )} + \frac{16}{{Re}_{s_{m\; i\; n}}}}} & {{Equation}\mspace{14mu} 17}\end{matrix}$

Equation 18 below illustrates fanning friction factor inside the annulusfor transitional flow.

$\begin{matrix}{f = {{( \frac{{Re} - {Re}_{a_{m\; i\; n}}}{800} )( {\frac{{\log_{10}\lbrack n_{s} \rbrack} + 3.93}{50\;{{Re}_{a_{\max}}}^{\lbrack\frac{1.75 - {\log_{10}{(n_{s})}}}{7}\rbrack}} - \frac{24}{{Re}_{a_{m\; i\; n}}}} )} + \frac{24}{{Re}_{a_{m\; i\; n}}}}} & {{Equation}\mspace{14mu} 18}\end{matrix}$

Equation 19 below illustrates fanning friction factor inside the drillpipe and drill collar for turbulent flow.

$\begin{matrix}{f = \frac{{\log_{10}( n_{s} )} + 3.93}{50\;{Re}^{(\frac{1.75 - {\log_{10}{\lbrack n_{s}\rbrack}}}{7})}}} & {{Equation}\mspace{14mu} 19}\end{matrix}$

Equation 20 below illustrates fanning friction factor inside the annulusfor turbulent flow.

$\begin{matrix}{f = \frac{{\log_{10}( n_{a} )} + 3.93}{50\;{Re}^{(\frac{1.75 - {\log_{10}{\lbrack n_{a}\rbrack}}}{7})}}} & {{Equation}\mspace{14mu} 20}\end{matrix}$

Notes: Inputs: n values are (dimensionless) and Reynolds numbers are(dimensionless). Output: Fanning friction factor is (dimensionless). Formore information on input and output values, please refer to the Table 2and Table 3, respectively.

Interface Requirements: No additional interface requirements.

7. Pressure Loss Gradient

The pressure loss gradient is a measure of how much pressure is lostacross a unit length of the hole depth (measured depth).

Equation 21 below illustrates pressure loss gradient inside the drillpipe and drill collar.

$\begin{matrix}{{\Delta\frac{p}{L}} = {{f( \frac{v}{60} )}^{2}( \frac{\rho}{25.81\; d} )}} & {{Equation}\mspace{14mu} 21}\end{matrix}$where d: drill pipe inside diameter OR drill collar inside diameter.

Equation 22 below illustrates pressure loss gradient inside the annulus.

$\begin{matrix}{{\Delta\frac{p}{L}} = {{f( \frac{v}{60} )}^{2}( \frac{\rho}{25.81\;( {d_{2} - d_{1}} )} )}} & {{Equation}\mspace{14mu} 22}\end{matrix}$where, OPEN HOLE:

d₁—drill pipe outside diameter OR drill collar outside diameter

d₂—drill bit outside diameter; and

where, CASED HOLE:

d₁—drill pipe outside diameter

d₂—casing diameter.

Notes: Inputs: diameters are measured in (in), mud weight is measured in

$( \frac{lb}{gal} ),$and velocity is measured in

$( \frac{ft}{\min} ).$Output: pressure loss gradient is measured in

$( \frac{psi}{ft} )$For more information on input and output values, please refer to theTable 2 and Table 3, respectively.

Interface Requirements: No interface Requirements.

8. Pressure Loss Due to Friction

The pressure loss due to friction is the pressure loss gradientmultiplied by the length of pipe of interest. The result of this productis the total pressure loss over that length of pipe.

Equation 23 below illustrates pressure loss due to friction inside thedrill pipe.

$\begin{matrix}{{\Delta\; p_{dp}} = {\Delta\;\frac{p}{L_{dp}}( L_{dp} )}} & {{Equation}\mspace{14mu} 23}\end{matrix}$

Equation 24 below illustrates pressure loss due to friction inside thedrill collar.

$\begin{matrix}{{\Delta\; p_{d\; c}} = {\Delta\;\frac{p}{L_{d\; c}}( L_{d\; c} )}} & {{Equation}\mspace{14mu} 24}\end{matrix}$

Equation 25 below illustrates pressure loss due to friction between thedrill pipe and casing.

$\begin{matrix}{{\Delta\; p_{dpc}} = {\Delta\;\frac{p}{L_{dpc}}( L_{c} )}} & {{Equation}\mspace{14mu} 25}\end{matrix}$

Equation 26 below illustrates pressure loss due to friction between thedrill pipe and open hole.

$\begin{matrix}{{\Delta\; p_{dph}} = {\Delta\;\frac{p}{L_{dpoh}}( {L_{dp} - L_{c}} )}} & {{Equation}\mspace{14mu} 26}\end{matrix}$

Equation 27 below illustrates pressure loss due to friction between thedrill collar and open hole.

$\begin{matrix}{{\Delta\; p_{dph}} = {\Delta\;\frac{p}{L_{dcoh}}( L_{d\; c} )}} & {{Equation}\mspace{14mu} 27}\end{matrix}$

Notes: Inputs: pressure loss gradient measured in

$( \frac{psi}{ft} )$and distance and length are measured in (ft). Output: pressure loss dueto friction is measured in (psi). For more information on input andoutput values, please refer to the Table 2 and Table 3, respectively.

Interface Requirements: No additional interface requirements.

9. Equivalent Circulating Density

The equivalent circulating density is defined as the effective densitythat the circulating fluid in the annulus exerts against the formation.

Equation 28 below illustrates equivalent circulating density.

$\begin{matrix}{{ECD} = {\rho + \frac{{\Delta\; p_{dpch}} + \Delta_{dpoh} + {\Delta\; p_{dcoh}}}{0.052\; D_{tvd}}}} & {{Equation}\mspace{14mu} 28}\end{matrix}$

Notes: Inputs: pressure loss due to friction is measured in (psi), mudweight is measured in

$( \frac{lb}{gal} ),$and distance is measured in (ft). Output: equivalent circulating densityis measured in

$( \frac{lb}{gal} ).$For more information on input and output values, please refer to theTable 2 and Table 3, respectively.

Interface Requirements: No additional interface requirements.

FIG. 7 illustrates an annular hydraulics display.

HYDRAULICS AT THE BIT

FIG. 8 illustrates hydraulics at the bit workflow. Inside each of theprocess boxes of the flowchart above, there are two numbers. The numberon the left represents the total number of outputs that come from thatsingle process. The number in parentheses on the right represents thenumber of outputs that are in real-time. There are 4 total inputs (1 RT)in this section that produces 6 total outputs (5 RT).

1. Total Flow Area

Total flow area represents the sum of the areas of the jets throughwhich fluid travels. This is a factor in calculating the jet velocity inthe next section.

Equation 29 below illustrates total flow area.

$\begin{matrix}{A = \frac{J_{1}^{2} + J_{2}^{2} + J_{3}^{2} + J_{4}^{2} + \ldots + J_{x}^{2}}{1303.8}} & {{Equation}\mspace{14mu} 29}\end{matrix}$

Notes: Input: jet diameter is measured in

$( \frac{in}{32} ).$Output: total flow area is measured in (in²). The subscript “x” in theequation above represents the x^(th) jet (the last jet in the series).For More information on input and output values, please refer to Table 2and Table 3, respectively.

Interface Requirements: In order to run this calculation, the interfaceneeds an input for the jet diameters. See FIG. 9 illustrating interfaceinputs for total flow area.

2. Jet Velocity

Jet velocity is a measure of how quickly fluid is travelling through thejets, and is determined by the volumetric flow rate and the total flowarea. It is the same for all jets, regardless of their individualdiameters.

Equation 30 below illustrates jet velocity.

$\begin{matrix}{v_{jet} = \frac{19.249\; Q}{A}} & {{Equation}\mspace{14mu} 30}\end{matrix}$

Notes: Inputs: total flow area is measured in (in²) and flow rate ismeasured in

$( \frac{gal}{\min} ).$Output: jet velocity is measured in

$( \frac{ft}{\min} ).$

For more information on input and output values, please refer to theTable 2 and Table 3, respectively.

Interface Requirements: No additional interface requirements.

3. Lost Pressure at the Bit

This pressure loss occurs as the fluid travels through the jet nozzlesand effects the overall hydraulic power of the bit. A nozzle coefficientof 0.95 is considered standard for this calculation and has beenincluded in the coefficients below.

Equation 31 below illustrates lost pressure at the bit.

$\begin{matrix}{{\Delta\; p_{b}} = \frac{156\;{\rho \cdot Q^{2}}}{( {1303.8\; A} )^{2}}} & {{Equation}\mspace{14mu} 31}\end{matrix}$

Notes: Inputs: total flow area is measured in (in²), mud weight ismeasured in

$( \frac{lb}{gal} ),$and flow rate is measured in

$( \frac{gal}{\min} ).$Output: pressure loss at the bit is measured in (psi). For moreinformation on input and output values, please refer to Table 2 andTable 3, respectively.

Interface Requirements: No additional interface requirements.

4. Hydraulic Power

Hydraulic power is a measure of energy per unit time that is availableto the bit during drilling as a result of the fluid travelling throughthe jets. Hydraulic power per unit area is also a measure of this, butis normalized to the hole area. Since some operators prefer the firstmeasurement and others prefer the second, both are included here.

Equation 32 below illustrates hydraulic power.

$\begin{matrix}{P = \frac{{Q \cdot \;\Delta}\; p_{b}}{1714}} & {{Equation}\mspace{14mu} 32}\end{matrix}$

Equation 33 below illustrates hydraulic power per unit area.

$\begin{matrix}{P_{A} = \frac{1.2732\; P}{d_{h}^{2}}} & {{Equation}\mspace{14mu} 33}\end{matrix}$

Notes: Inputs: pressure loss at the bit is measured in (psi), bitoutside diameter is measured in (in), and flow rate is measured in

$( \frac{gal}{\min} ).$Outputs: power is measured in (hp) and power per unit area is measuredin

$( \frac{hp}{{in}^{2}} ).$For more information on input and output values, please refer to theTable 2 and Table 3, respectively.

Interface Requirements: No additional interface requirements.

5. Impact Force

Impact force is a measure of the force applied to the formation by thefluid coming out of the jets. It is used as another way of determiningbit power.

Equation 34 below illustrates impact force.

$\begin{matrix}{F_{i} = \frac{\rho \cdot Q \cdot v_{jet}}{115920}} & {{Equation}\mspace{14mu} 34}\end{matrix}$

Notes: Inputs: velocity is measured in

$( \frac{ft}{\min} ),$mud weight is measured in

$( \frac{lb}{gal} ),$and the flow rate is measured in

$( \frac{gal}{\min} ).$Output: impact force is measured in (lbF). For more information on inputand output values, please refer to the Table 2 and Table 3,respectively.

Interface Requirements: No additional interface requirements.

FIG. 10 illustrates hydraulics at the bit display.

CUTTING TRANSPORTATION

FIG. 11 illustrates a cutting transportation workflow. Inside each ofthe process boxes of the flowchart on the right, there are two numbers.The number on the left represents the total number of outputs that comefrom that single process. The number in parentheses on the rightrepresents the number of outputs that are in real-time. There are 11total inputs (5 RT) in this section that produce 14 total outputs (14RT).

1. Boundary Shear Rate

The boundary shear rate is a measure of the velocity change per unitdistance experienced by the fluid at the wall of the hole.

Equation 35 below illustrates boundary shear rate.

$\begin{matrix}{\gamma_{b} = \frac{186}{d_{cut} \cdot \rho^{0.5}}} & {{Equation}\mspace{14mu} 35}\end{matrix}$

Notes: Inputs: average particle diameter is measured in (in) and mudweight is measured in

$( \frac{lb}{gal} ).$Output: boundary shear rate is measured in (s⁻¹). For more informationon input and output values, please refer to the Table 2 and Table 3,respectively.

Interface Requirements: The bound shear rate calculations uses theaverage cutting diameter. The interface accepts this value as an input.See FIG. 12 illustrating interface inputs for boundary shear rate.

2. Shear Stress Developed by the Particle

The shear stress developed by the particle is a measure of the forceapplied by the particle on the fluid.

Equation 36 below illustrates shear stress developed by the particle.

$\begin{matrix}{\tau_{p} = {7.9\lbrack {T( {20.8 - \rho} )} \rbrack}^{0.5}} & {{Equation}\mspace{14mu} 36}\end{matrix}$

Notes: Inputs: average particle thickness is measured in (in) and mudweight is measured in

$( \frac{lb}{gal} ).$Output: particle shear stress is measured in

$( \frac{lbF}{100\mspace{14mu}{ft}^{2}} )$For more information on input and output values, please refer to theTable 2 and Table 3, respectively.

Interface Requirements: The average cutting thickness is an input thatthe interface accounts for. See FIG. 13 illustrating interface inputsfor shear stress developed by the particle.

3. Shear Rate Developed by the Particle

The shear rate developed by the particle is a measure of the velocitychange per unit distance experienced by the fluid as a result of theparticle.

Equation 37 below illustrates shear rate developed by the particle.

$\begin{matrix}{\gamma_{p} = ( \frac{\tau_{p}}{k_{a}} )^{\frac{1}{n_{a}}}} & {{Equation}\mspace{14mu} 37}\end{matrix}$

Notes: Input: particle shear stress is measured in

$( \frac{lbF}{100\mspace{14mu}{ft}^{2}} ),$the ‘n’ power law constant is (dimensionless), and the ‘k’ power lawconstant is measured in (P). Output: particle shear rate is measured in(s⁻¹). The regime is considered laminar if γ_(p)≤γ_(b) and turbulent ifγ_(p)>γ_(b). For more information on input and output values, pleaserefer to the Table 2 and Table 3, respectively.

Interface Requirements: No additional interface requirements.

4. Slip Velocity

The slip velocity is the rate at which the particles tend to falltowards the drill bit. It is the component of the overall transportvelocity that counteracts the fluid's annular velocity.

Equation 38 below illustrates slip velocity for laminar flow.

$\begin{matrix}{v_{s} = {1.22\;{\tau_{p}( \frac{\gamma_{p} \cdot d_{cut}}{\rho^{0.5}} )}^{0.5}}} & {{Equation}\mspace{14mu} 38}\end{matrix}$

Equation 39 below illustrates slip velocity for turbulent flow.

$\begin{matrix}{v_{s} = \frac{16.62\;\tau_{p}}{\rho^{0.5}}} & {{Equation}\mspace{14mu} 39}\end{matrix}$

Note: Inputs: particle shear stress is measured in (lbF), particle shearrate is measured in (s⁻¹), average particle diameter is measured in(in), and mud weight is measured in

$( \frac{lb}{gal} ).$Output: slip velocity is measured in

$( \frac{ft}{\min} ).$For more information on input and output values, please refer to Table 2and Table 3, respectively.

Interface Requirements: No additional interface requirements.

5. Transport Velocity

The transport velocity is the net rate at which the cutting particlestravel from the bit to the surface of the hole.

Equation 40 below illustrates transport velocity.

$\begin{matrix}{v_{t} = {v - v_{s}}} & {{Equation}\mspace{14mu} 40}\end{matrix}$

Notes: Inputs: annular velocity is measured in

$( \frac{ft}{\min} ).$and slip velocity is measured in

$( \frac{ft}{\min} ).$Output: transport velocity is measured in

$( \frac{ft}{\min} ).$This value can be positive. Negative values mean that the cuttingparticles are travelling down towards the drill bit which could causestuck pipe, among other problems. For more information on input andoutput values, please refer to Table 2 and Table 3, respectively.

Interface Requirements: No additional interface requirements.

6. Transport Efficiency

The transport efficiency is the ratio of the transport velocity to theannular velocity. This value approaching 100% represents more efficientcutting transport efficiency.

Equation 41 below illustrates transport efficiency.

$\begin{matrix}{E_{t} = {\frac{v_{t}}{v} \times 100}} & {{Equation}\mspace{14mu} 41}\end{matrix}$

Notes: Inputs: annular velocity is measured in

$( \frac{ft}{\min} )$and transport velocity is measured in

$( \frac{ft}{\min} ).$Output: transport efficiency is measured in (%). For more information oninput and output values, please refer to Table 2 and Table 3,respectively.

Interface Requirements: No additional interface requirements.

7. Cutting Concentration

The cuttings concentration is the ratio of cuttings to annular volume.At high concentrations many problems can occur including stuck pipe,among other things.

Equation 42 below illustrate cuttings concentration.

$\begin{matrix}{C = {\frac{({ROP})d_{h}^{2}}{14.71\;{E_{t} \cdot Q}} \times 100}} & {{Equation}\mspace{14mu} 42}\end{matrix}$

Notes: Input: hole diameter is measured in (in), rate of penetration ismeasured in

$( \frac{ft}{hr} )$transport efficiency is measured in (%), and flow rate is measured in

$( \frac{gal}{\min} ).$Output: cuttings concentration is measured in (%). For more informationon input and output values, please refer to the Table 2 and Table 3,respectively.

Interface Requirements: No additional interface requirements.

FIG. 14 illustrates a cutting transportation display.

SWAB AND SURGE

FIG. 15 illustrates a swab and surge workflow. Inside each of theprocess boxes of the flowchart on the right, there are two numbers. Thenumber on the left represents the total number of outputs that come fromthat single process. The number in parentheses on the right representsthe number of outputs that are in real-time. There are 16 total inputs(3 RT) in this section that produce 28 total outputs (22 RT).

Swab and surge do not occur during the drilling process, unlike theother three major analyses. This means that many values that have beencalculated before are recalculated for the new conditions. It needs tobe determined if swab is occurring, surge is occurring, or neither are.For this current bit depth, D_(bc), and the most recent previous bitdepths, D_(bp) are known.

1. Average Maximum Speed of Pipe Movement and Equivalent Fluid Velocity

The average maximum speed of pipe movement is the highest approximatespeed the drill string will obtain while tripping out. The equivalentfluid velocity is the velocity of the stationary fluid relative to themoving pipe during these procedures.

Equation 43 below illustrates average maximum speed of pipe movement.

$\begin{matrix}{v_{p} = \frac{90\; L_{s}}{t}} & {{Equation}\mspace{14mu} 43}\end{matrix}$

Equation 44 below illustrates equivalent fluid velocity.

$\begin{matrix}{v_{e} = {v_{p}( {0.45 + \frac{d_{1}^{2}}{d_{2}^{2} - d_{1}^{2}}} )}} & {{Equation}\mspace{14mu} 44}\end{matrix}$where, OPEN HOLE:

d₁—drill pipe outside diameter OR drill collar outside diameter

d₂—drill bit outside diameter; and

where, CASED HOLE:

d₁—drill pipe outside diameter

d₂—casing diameter.

Notes: Inputs: stand length is measured in (ft), time from slips toslips is measured in (s), and all diameters are measured in (in).Outputs: average maximum speed of pipe movement is measured in

$( \frac{ft}{\min} )$and equivalent fluid velocity is measured in

$( \frac{ft}{\min} ).$For more information on input and output values, please refer to theTable 2 and Table 3, respectively.

Interface Requirements: To calculate the maximum average speed of pipemovement, the stand length and the time from slips to slips can beknown. See FIG. 16 illustrating interface inputs for average maximumspeed of pipe movement and equivalent fluid velocity.

2. Effective Viscosity

The effective viscosity is recalculated inside the annulus from toaccount for the equivalent fluid velocities as opposed to the annularvelocities.

Equation 45 below illustrates effective viscosity inside the annulus.

$\begin{matrix}{\mu = {100\;{k_{a}\lbrack \frac{144\; v_{e}}{60( {d_{2} - d_{1}} )} \rbrack}^{n_{a} - 1}}} & {{Equation}\mspace{14mu} 45}\end{matrix}$where, OPEN HOLE:

d₁—drill pipe outside diameter OR drill collar outside diameter

d₂—drill bit outside diameter; and

where, CASED HOLE:

d₁—drill pipe outside diameter

d₂—casing diameter.

Notes: Inputs: all diameters are measured in (in) and velocity ismeasured in

$( \frac{ft}{\min} ).$Output: viscosity is measured in (cP). For more information on input andoutput values, please refer to the Table 2 and Table 3, respectively.

Interface Requirements: No additional interface requirements.

3. Flow Regime

Reynolds number is recalculated for the equivalent fluid velocity andfor any new diameters. The critical values only need to be recalculatedin the fluid properties have changed.

Equation 46 below illustrates Reynolds number inside the annulus.

$\begin{matrix}{{Re} = \frac{928{v_{e}( {d_{2} - d_{1}} )}\rho}{60\;{\mu( \frac{{2n_{a}} + 1}{3\; n_{a}} )}^{n_{a}}}} & {{Equation}\mspace{14mu} 46}\end{matrix}$

Equation 47 below illustrates minimum critical Reynolds number.

$\begin{matrix}{{Re}_{\min} = {3470 - {1370\; n}}} & {{Equation}\mspace{14mu} 47}\end{matrix}$

Equation 48 below illustrates maximum critical Reynolds number.

$\begin{matrix}{{Re}_{\max} = {4270 - {1370\; n}}} & {{Equation}\mspace{14mu} 48}\end{matrix}$

Notes: Inputs: diameters are measured in (in), n values are(dimensionless), k values are measured in (P), Reynolds numbers are(dimensionless), mud weight is measured in

$( \frac{lb}{gal} ),$and velocity is measured in

$( \frac{ft}{\min} ).$Outputs: Reynolds numbers are (dimensionless), velocity is measured in

$( \frac{ft}{\min} ),$and annular flow rate is measured in

$( \frac{gal}{\min} ).$If the Reynolds number is: (a) below the minimum critical values, theflow is laminar; (b) between the minimum and maximum, the flow istransitional; and (c) above the maximum, the flow is turbulent. For moreinformation on input and output values, please refer to the Table 2 andTable 3, respectively.

Interface Requirements: No additional interface requirements.

4. Swab or Surge Pressure

The swab and surge pressure losses are equivalent to the pressure lossdue to friction analysis.

Equation 49 below illustrates fanning friction factor inside the annulusfor laminar flow.

$\begin{matrix}{f = \frac{24}{Re}} & {{Equation}\mspace{14mu} 49}\end{matrix}$

Equation 50 below illustrates fanning friction factor inside the annulusfor transitional flow.

$\begin{matrix}{f = {{( \frac{{Re} - {Re}_{a_{\min}}}{800} )( {\frac{{\log_{10}\lbrack n_{a} \rbrack} + 3.93}{50\;{{Re}_{a_{\max}}}^{\lbrack\frac{1.75 - {\log_{10}{(n_{a})}}}{7}\rbrack}} - \frac{24}{{Re}_{a_{m\; i\; n}}}} )} + \frac{24}{{Re}_{a_{m\; i\; n}}}}} & {{Equation}\mspace{14mu} 50}\end{matrix}$

Equation 51 below illustrates fanning friction factor inside the annulusfor turbulent flow.

$\begin{matrix}{f = \frac{{\log_{10}( n_{a} )} + 3.93}{50\;{Re}^{\lbrack\frac{1.75 - {\log_{10}{(n_{a})}}}{7}\rbrack}}} & {{Equation}\mspace{14mu} 51}\end{matrix}$

Equation 52 below illustrates pressure loss gradient inside the annulus.

$\begin{matrix}{\frac{\Delta\; p}{\Delta\; L} = {{f( \frac{v}{60} )}^{2}( \frac{\rho}{25.81( {d_{2} - d_{1}} )} )}} & {{Equation}\mspace{14mu} 52}\end{matrix}$

Equation 53 below illustrates pressure loss due to swab or surge betweenthe drill pipe and casing.

$\begin{matrix}{{\Delta\; p_{dpc}} = {\frac{\Delta\; p}{\Delta\; L_{dpc}}( L_{c} )}} & {{Equation}\mspace{14mu} 53}\end{matrix}$

Equation 54 below illustrates pressure loss due to swab or surge betweenthe drill pipe and open hole.

$\begin{matrix}{{\Delta\; p_{dph}} = {\frac{\Delta\; p}{\Delta\; L_{dph}}( {L_{dp} - L_{c}} )}} & {{Equation}\mspace{14mu} 54}\end{matrix}$

Equation 55 below illustrates pressure loss due to swab or surge betweenthe drill collar and open hole.

$\begin{matrix}{{\Delta\; p_{dch}} = {\frac{\Delta\; p}{\Delta\; L_{dch}}( L_{d\; c} )}} & {{Equation}\mspace{14mu} 55}\end{matrix}$

Notes: Inputs: diameters are measured in (in), n values are(dimensionless), Reynolds numbers are (dimensionless), mud weight ismeasured in

$( \frac{lb}{gal} ),$velocity is measured in

$( \frac{ft}{\min} ),$lengths and distances are measured (ft). Outputs: fanning frictionfactors are (dimensionless), pressure loss gradient is measured in

$( \frac{psi}{ft} ),$and pressure loss due to friction is measured in (psi). For moreinformation on input and output values, please refer to the Table 2 andTable 3, respectively.

Interface Requirements: No additional interface requirements.

5. Gel-Breaking Pressure

The gel-breaking pressure is the approximate pressure required to pushthe pipe into the stationary mud after a trip.

Equation 56 below illustrates gel-breaking pressure.

$\begin{matrix}{p_{g} = \frac{4{L \cdot \tau_{30}}}{1200( {d_{2} - d_{1}} )}} & {{Equation}\mspace{14mu} 56}\end{matrix}$

Notes: Inputs: annular section length is measured in (ft) and 30-minutegel strength is measured in

$( \frac{lbF}{100\mspace{14mu}{ft}^{2}} ).$

Output: gel-breaking pressure is measured in (psi). For more informationon input and output values, please refer to the Table 2 and Table 3,respectively.

Interface Requirements: The 30-minute gel strength is used to performthe gel-breaking pressure calculation. See FIG. 17 illustratinginterface inputs for gel-breaking pressure.

6. Equivalent Mud Weight

The equivalent mud weight is an adjusted value similar to equivalentcirculating density that accounts for the pressure losses due to swaband surge. The higher of the two values (gel-breaking pressure orpressure loss due to friction) is needed to calculate this value. Thepressure used may vary between annular sections. Δ_(p) ₁ , Δ_(p) ₂ , andΔ_(p) ₃ represent the values that have been selected for each annularsection.

Equation 57 below illustrates equivalent mud weight (swab).

$\begin{matrix}{\rho_{e} = {\rho - \frac{{\Delta\; p_{1}} + {\Delta\; p_{2}} + {\Delta\; p_{3}}}{0.052\; D_{tvd}}}} & {{Equation}\mspace{14mu} 57}\end{matrix}$

Equation 58 below illustrates equivalent mud weight (surge).

$\begin{matrix}{\rho_{e} = {\rho - \frac{{\Delta\; p_{1}} + {\Delta\; p_{2}} + {\Delta\; p_{3}}}{0.052\; D_{tvd}}}} & {{Equation}\mspace{14mu} 58}\end{matrix}$

Notes: Inputs: pressure loss due to friction is measured in (psi), mudweight is measured in

$( \frac{lb}{gal} ),$and distance is measured in (ft). Output: equivalent mud weight ismeasured in

$( \frac{lb}{gal} ).$For more information on input and output values, please refer to theTable 2 and Table 3, respectively.

Interface Requirements: No additional interface requirements.

FIG. 18 illustrates a swab and surge display.

FIG. 19 illustrates a technical workflow. Inside several of the processboxes of the flowchart on the right, there are two numbers. The numberon the left represents the total number of outputs that come from thatsingle process. The number in parentheses on the right represents thenumber of outputs that are in real-time. There are 25 total inputs (7RT) in total that produce 98 total outputs (77 RT). To utilize the fullpower of the calculation engine and to provide the best service possibleto the operator, the interface includes a unit selection component thattells the calculation engine when it is to perform unit conversionoperations.

TORQUE & DRAG SURVEILLANCE SUITE IN REAL-TIME

The real-time torque and drag analysis surveillance suite allows for acomparison of the planned and actual performance of the drill stringbecause it provides an instantaneous analysis in real-time. The systemcan display, compare, and evaluate the hookload, friction force, andreal friction coefficient in real-time based on other parametersincluding friction coefficients planned, activity code (RIH, ROT, POH),BHA weight, mud density, drill pipe OD, and trajectory performance.

The severity cross plot which is included in the system allows anevaluation of the changes observed in the hookload and friction factoranalysis whilst monitoring the trajectory performance. The systemincludes algorithms to calculate the actual friction coefficient on thewell for inclined and lateral sections. The hookload and friction factorsystem can detect and display individual hookloads when the well istripping-in, tripping-out, and rotating.

This solution allows input data to be calculated and updated in realtime. This solution allows for the integration of real-time and non-realtime inputs within a real-time system. This means that this solutionallows a direct comparison between the planned and actual values forvariables such as hookload. Another unique feature of this solution isthat the model for the planned values can be updates quickly and easily,as they are needed, through the use of correction factors. This takes alot less time than having to adjust the calculations in the model tocalibrate the system.

The real-time torque and drag surveillance suite allows a drillingcompany to improve the efficiency of their drilling behavior in terms ofboth time and money and reduce the safety risk to their staff. Thissolution updates its outputs within a matter of seconds. This is muchfaster than any other solution available for the same purpose. Thismeans that the display that the customer vies show data that is muchmore accurate to the actual conditions in the well at the time it'sviewed. The consequence of this is that the scale of the risk is thedecision making process is significantly reduced thus lessening thechance that problems such-as stuck pipe, blowouts, and landslides willoccur.

This solution is built on WITSML, the standard for drilling-dataexchange in the oil and gas industry. Since WITSML is used by manydifferent programs this solution allows a large degree of integrationbetween different systems which gives the flexibility necessary formodern drilling. Basing the solution on WITSML also means it is easy forcustomers to share data with partner firms and any other group.

It allows multi-rig data flow, and takes advantage of back up serverswhich ensure the well has zero down time. Rig analytics reports, 24/7remote monitoring, and custom alerts mean that customers can always havetheir fingers on the pulse of their wells; they can even access displayson their tablet or smart phone.

The solution is also highly customizable since both the visualizationand real-time calculations can be tailored to the customer's individualneeds. The real-time displays show a multitude of information at aglance with tabs that enable effortless toggling between them.

SUMMARY OF INPUTS

Table 6 illustrates the inputs that process the outputs for the overalltorque and drag analysis. The name of every input is given, along withits respective symbol, its units, whether the data collected is inreal-time (RT), or not in real-time (NRT) and whether the data iscollected on the surface and/or down the hole. The abbreviation N/A inTable 6 and Table 7 stand for not applicable. Table 6 below summarizesthe inputs to the real-time Torque and Drag Solution.

TABLE 6 Surface/ # Input Symbol Unit RT/NRT Downhole 1. Total Drillstring Weight N/A lb/ft NRT Surface 2, Mud Weight μ lbF NRT Surface 3.Buoyancy Factor BF N/A NRT Surface 4, Top Drive Weight N/A lbF NRTSurface 5. Friction Coefficient μ N/A NRT Surface 6. Kick-off PointDepth KOP ft NRT Surface 7. Last Casing Depth N/A ft NRT Surface 8.Current Section N/A N/A NRT Surface 9. Measured Depth MD ft RT Downhole10. Incline Inc Rad RT Downhole 11. Azimuth Azi Rad RT Downhole 12. DogLeg Severity DLS °/100 ft RT Downhole 13. Drill Pipe Outside OD InchesNRT Surface Diameter 14. Bottom Hole Assembly BHA IbF NRT Surface Weight

SUMMARY OF OUTPUTS

Table 7 contains all the outputs of the torque and drag analysis. Itfollows a similar format to Table 6. Table 7 below summarizes theoutputs from the real-time torque and drag solution.

TABLE 7 # Outputs Symbol Units RT/NRT 1. Actual Inclination Inc. AverRad RT 2. Slack off Hookload (μ = 0.1) N/A Kips RT 3. Slack off Hookload(μ = 0.2) N/A Kips RT 4. Slack off Hookload (μ =0.3) N/A Kips RT 5. Pickup Hookload (μ = 0.1) N/A Kips RT 6. Pick up Hookload (μ = 0.2) N/A KipsRT 7. Pick up Hookload (μ = 0.3) N/A Kips RT 8 Torque OHFF (μ = 0.1) N/AFt-lbf RT 9. Torque OHFF (μ = 0.2) N/A Ft-lbf RT 10. Torque OHFF (μ =0.3) N/A Ft-lbf RT 14. Torque OHFF (μ = 0.4) N/A Ft-lbf RT

REAL-TIME TORQUE AND DRAG SOLUTION

The torque and drag solution is a real-time optimization solution topredict and evaluate the performance of a particular drilling situation.The system allows customers to view ‘broomstick,’ style graphs which arecreated in real-time. These graphs are created for hookload, frictionforce, friction factor, and torque. The broomstick displays compare theplanned effects with the actual effects computed in real-time from themeasurements made at the drill site. The system performs the hookload,friction factor, and torque and drag analyses with six subsystems.

FIG. 20 illustrates the movement of variables through the system and theinterdependency of the subsystems.

System 1. Drill String Load Analysis per Section

For analysis, the drill string is split into four sections, each with adifferent weight per foot value. Section 1 is the BHA and the sectionnumber increases with distance from the bit. System 1 computes theweight of the drill string for each section by multiplying the weightper foot for that section of drill string by the length in feet of thatsection. See FIG. 21 illustrating a diagram to explain the numbering ofBHA sections.

System 2. Action Selector

The action selector system has an input which is the action that thedrill string is performing at an instant. The drilling activities thatcan occur are tripping in, rotating and tripping out. An explanation ofthe drilling activities can be seen in FIG. 22 illustrating a diagram toshow the number assigned to each activity. System 2 transforms theaction into an input to System 4, discussed below, which allows for thecorrect equation to be used to calculate the forces of friction andtension for each section.

System 3. Wellbore Condition Selector

The wellbore condition selector system has an input which is thecondition that the wellbore is in at an instant. The wellbore conditionsthat can occur are vertical, build-up, hold, and drop-off. Anexplanation of the wellbore conditions can be seen in FIG. 23illustrating a diagram to show the numbers assigned to each wellborecondition. System 3 transforms the action into an input to System 4,discussed below, which allows for the correct equation to be used tocalculate the forces of friction and tension for each section.

System 4. Equation Locator

The equation locator system used the outputs from System 2 and System 3to choose the correct equations to use to calculate the hookload foreach specific condition. Table 8, shown below, shows the equations usedby System 4 for different action and conditions.

TABLE 8 Wellbore Action Condition Equation Equation for Change inEquation for Normal Selector Selector Code Tension ΔT (lbf) ReactionForce N (lbf) System 2 System 3 System 4 System 5 System 5 Tripping inDrop-Off A1 ΔT = Wcos(l) − μ[Wsin(l) + N = Wsin(l) + 2Tsin(δ/2) (RIH)2Tsin (δ/2)] Build-Up A2 ΔT = Wcos(l) − μ[Wsin(l) − N = Wsin(l) −2Tsin(δ/2) 2Tsin (δ/2)] Hold A3 ΔT = Wcos(l) + μWsin(l) N = Wsin(l)Rotating Drop-Off ΔT = Wcos(l) N = Wsin(l) + 2Tsin(δ/2) Build-Up B2 ΔT =Wcos(l) N = Wsin(l) − 2Tsin(δ/2) Hold B3 ΔT = Wcos(l) + μWsin(l) N =Wsin(l) Tripping Drop-Off C1 ΔT = Wcos(l) + μ[Wsin(l) + N = Ws/n(l) +2Tsin(δ/2) Out (POH) 2Tsin(δ/2) Build-Up C2 ΔT = Wcos(l) + μ|Wsin(l) − N= Wsin(l) − 2Tsin(δ/2) 2Tsin(δ/2)| Hold C3 ΔT = Wcos(L) + μWsin(l) N =Wsin(l)

System 5. Hooked Analysis

System 5 used the correct equation for each set of data as specified bysystem 4 to perform the hookload analysis. System 5 also used bothreal-time and non-real-time data for inputs.

System 6. Torque Analysis

System 6 used the correct equation for each set of data as specified bySystem 4 to perform the torque analysis. System 6 also used bothreal-time and non-real-time data for inputs.

Correction Factors

Correction factors are used to calibrate measured field data in order toimprove the accuracy of the data used in calculations. In thecalculation engine a correction factor is used for the hookload.

The correction factor used for the hookload is a percentage value. Thepick-up hookload is found in the calculation engine by multiplying thetripping out hookload force by 100% plus the percentage hookloadcorrection factor.

Table 9 below shows the magnitude of the correction factors used andwhether the original values is increased by a percentage correctionfactor or whether the original value is increased by addition of thecorrection factor.

TABLE 9 Output to be Corrected: Type of Correction Value Hook Percentage18% Torque Addition 3500 Case Hole Percentage 10%

In practice, correction factors change whenever the drilling conditionschange, for example, when a section of the drill string is changed.

CONSOLE DISPLAYS

FIG. 24 shows an example of the real-time display console that canprovide for torque and drag analysis. This particular display has thehookload broomstick as the first graph from the left and the torquebroomstick as the second display from the left. It also has displays fortrajectory and dogleg severity. FIG. 25 shows an alternative displaywith the broomstick graphs displayed horizontally.

FIG. 26 illustrates an example of the hookload and friction factordisplay. FIG. 26 shows that the largest section of the console displayis made up of three graphs that compare the actual values to the plannedvalues for hookload, friction force, and friction coefficient. Thedisplay includes three smaller plots for the wellbore trajectory: (1)showing the wellbore trajectory as a whole in three dimensions; (2) ‘NSvs. EW,’ showing the angle of the drill string; and (3) ‘TVD vs. VS,’showing the relationship between the true vertical depth and thevertical section. Each of these has curves for both planned and actualvalue. There is also a small diagram to display the block height and oneto indicate whether the drill string is on bottom or off bottom.Finally, there is a display to show how the dogleg severity of the drillstring varies with the measured depth.

FIG. 27 shows a display that combines the graphs from the torque anddrag display and the graphs from the hookload and friction factordisplay. FIGS. 28-31 illustrate additional displays according to thepresent disclosure.

Depending on the embodiment, certain acts, events, or functions of anyof the algorithms described herein can be performed in a differentsequence, can be added, merged, or left out altogether (e.g., not alldescribed acts or events are necessary for the practice of thealgorithms). Moreover, in certain embodiments, acts or events can beperformed concurrently, e.g., through multi-threaded processing,interrupt processing, or multiple processors or processor cores or onother parallel architectures, rather than sequentially. Although certaincomputer-implemented tasks are described as being performed by aparticular entity, other embodiments are possible in which these tasksare performed by a different entity.

Conditional language used herein, such as, among others, “can,” “might,”“may,” “e.g.,” and the like, unless specifically stated otherwise, orotherwise understood within the context as used, is generally intendedto convey that certain embodiments include, while other embodiments donot include, certain features, elements and/or states. Thus, suchconditional language is not generally intended to imply that features,elements and/or states are in any way required for one or moreembodiments or that one or more embodiments necessarily include logicfor deciding, with or without author input or prompting, whether thesefeatures, elements and/or states are included or are to be performed inany particular embodiment.

While the above detailed description has shown, described, and pointedout novel features as applied to various embodiments, it will beunderstood that various omissions, substitutions, and changes in theform and details of the devices or algorithms illustrated can be madewithout departing from the spirit of the disclosure. As will berecognized, the processes described herein can be embodied within a formthat does not provide all of the features and benefits set forth herein,as some features can be used or practiced separately from others. Thescope of protection is defined by the appended claims rather than by theforegoing description. All changes which come within the meaning andrange of equivalency of the claims are to be embraced within theirscope.

What is claimed is:
 1. A method comprising, by a computer system:receiving planned well-performance modeling data for a well currentlybeing drilled; receiving non-real-time data inputs in relation to thewell; receiving real-time data inputs produced by sensors in relation tothe well; receiving a correction factor that is indicative of drillingconditions; calibrating the real-time data inputs based, at least inpart, on the correction factor; determining well performance based, atleast in part, on the non-real-time data inputs and the calibratedreal-time data inputs; comparing, in real-time, the determined wellperformance with the planned well-performance modeling data for thewell; updating, in real-time, the planned well-performance modeling datafor the well based, at least in part, on the correction factor; andfacilitating a real-time display of comparison data for the well,wherein the real-time display comprises information related to thedetermined well performance and the updated planned well-performancemodeling data for the well.
 2. The method of claim 1, wherein thereal-time display of comparison data for the well comprises the plannedwell-performance modeling data for the well.
 3. The method of claim 1,wherein the facilitating comprises sending the real-time display ofcomparison data for the well to a remote client.
 4. The method of claim1, wherein the determining comprises executing a real-time torque anddrag analysis, wherein the executing the real-time torque and draganalysis comprises, in real-time: determining drill string load for eachsection of a drill string based, at least in part, on the non-real-timedata inputs and the calibrated real-time data inputs; determiningdrilling activity based, at least in part, on the non-real-time datainputs and the calibrated real-time data inputs, wherein the drillingactivity comprises tripping in, rotating and tripping out; determiningwellbore conditions based, at least in part, on the non-real-time datainputs and the calibrated real-time data inputs, wherein the wellboreconditions comprises vertical, build-up, hold and drop off; generatinghook load analysis using at least one of the determined drillingactivity and the determined wellbore conditions; and generating torqueand drag analysis using at least one of the determined drilling activityand the determined wellbore conditions.
 5. The method of claim 1,wherein the determining comprises executing a real-time annularhydraulics analysis, wherein the executing the real-time annularhydraulics analysis comprises, in real-time: determining a velocity of afluid based, at least in part, on the non-real-time data inputs and thecalibrated real-time data inputs, wherein the determined velocity of thefluid comprises a rate at which the fluid changes position over timewithin an annulus of the well; determining an effective viscosity of thefluid using the determined velocity of the fluid; determining a ratiobetween inertial and viscous forces based, at least in part, on thenon-real-time data inputs and the calibrated real-time data inputs;determining an annular critical velocity and an annular critical flowrate using the determined ratio; determining a fanning friction factorusing the determined ratio based, at least in part, on the non-real-timedata inputs and the calibrated real-time data inputs; determining apressure loss gradient using the fanning friction factor, wherein thepressure loss gradient comprises the pressure lost across a unit lengthof measured depth; determining pressure loss due to friction using thedetermined pressure loss gradient; and determining an effective densitythat the fluid exerts against a formation in the well.
 6. The method ofclaim 5, wherein the executing the real-time annular hydraulics analysiscomprises, in real-time: determining a sum of areas of at least one jetthrough which the fluid travels based, at least in part, on thenon-real-time data inputs and the calibrated real-time data inputs;determining a rate at which the fluid is traveling through the at leastone jet using the determined sum of areas, wherein the determined rateat which the fluid is traveling through the at least one jet produces ajet velocity; determining a pressure loss as the fluid travels throughthe at least one jet; determining hydraulic power using the determinedpressure loss, wherein the hydraulic power is a measure of energy perunit time that is available to a drill bit as a result of the fluidtravelling through the at least one jet; and determining impact forceapplied to the formation using the jet velocity.
 7. The method of claim5, wherein the executing the real-time annular hydraulics analysiscomprises, in real-time: determining a boundary sheer rate based, atleast in part, on the non-real-time data inputs and the calibratedreal-time data inputs, wherein the boundary sheer rate is a measure ofvelocity change per unit distance experienced by the fluid at a wall ofthe well; determining a shear stress developed by a particle based, atleast in part, on the non-real-time data inputs and the calibratedreal-time data inputs, wherein the shear stress developed by theparticle is a measure of force applied by the particle on the fluid;determining a shear rate developed by the particle based, at least inpart, on the non-real-time data inputs and the calibrated real-time datainputs, wherein the shear rate developed by the particle is a measure ofvelocity change per unit distance experienced by the fluid as a resultof the particle; determining a slip velocity using at least one of thedetermined shear stress developed by the particle and the determinedshear rate developed by the particle, wherein the slip velocity is ameasure of rate at which the particle tends to fall towards a drill bit;determining a transport velocity using the determined slip velocity,wherein the transport velocity is a net rate at which the particletravels from the drill bit to a surface of the well; determiningtransport efficiency based, at least in part, on the non-real-time datainputs and the calibrated real-time data inputs, wherein the transportefficiency is a ratio of the determined transport velocity to thedetermined velocity of the fluid within the annulus of the well; anddetermining cutting concentration based, at least in part, on thenon-real-time data inputs and the calibrated real-time data inputs,wherein the cutting concentration is a ratio of the particles in theannulus of the well to a total annular volume of the well.
 8. The methodof claim 5, wherein the executing the real-time annular hydraulicsanalysis comprises, in real-time: determining an average maximum speedof pipe movement based, at least in part, on the non-real-time datainputs and the calibrated real-time data inputs; determine an equivalentfluid velocity using the determined average maximum speed of pipemovement; determining an effective annular viscosity of the fluid usingthe determined equivalent fluid velocity; determining an annular ratiobetween inertial and viscous forces based, at least in part, on thenon-real-time data inputs and the calibrated real-time data inputs;determining an annular fanning friction factor using the determinedannular ratio based, at least in part, on the non-real-time data inputsand the calibrated real-time data inputs; determining annular pressureloss gradient using the annular fanning friction factor; determining atleast one of swabbing friction loss and surging friction loss using thedetermined annular pressure loss gradient; determining a gel-breakingpressure, wherein the gel-breaking pressure is a required force to pusha pipe into a stationary fluid in the well; and determining anequivalent fluid weight using at least one of the gel-breaking pressureand the at least one of swabbing friction loss and surging frictionloss.
 9. A system comprising a processor and memory, wherein theprocessor and memory in combination are operable to implement a methodcomprising: receiving planned well-performance modeling data for a wellcurrently being drilled; receiving non-real-time data inputs in relationto the well; receiving real-time data inputs produced by sensors inrelation to the well; receiving a correction factor that is indicativeof drilling conditions; calibrating the real-time data inputs based, atleast in part, on the correction factor; determining well performancebased, at least in part, on the non-real-time data inputs and thecalibrated real-time data inputs; comparing, in real-time, thedetermined well performance with the planned well-performance modelingdata for the well; updating, in real-time, the planned well-performancemodeling data for the well based, at least in part, on the correctionfactor; and facilitating a real-time display of comparison data for thewell, wherein the real-time display comprises information related to thedetermined well performance and the updated planned well-performancemodeling data for the well.
 10. The system of claim 9, wherein thedetermining comprises executing a real-time torque and drag analysis,wherein the executing the real-time torque and drag analysis comprises,in real-time: determining drill string load for each section of a drillstring based, at least in part, on the non-real-time data inputs and thecalibrated real-time data inputs; determining drilling activity based,at least in part, on the non-real-time data inputs and the calibratedreal-time data inputs, wherein the drilling activity comprises trippingin, rotating and tripping out; determining wellbore conditions based, atleast in part, on the non-real-time data inputs and the calibratedreal-time data inputs, wherein the wellbore conditions comprisesvertical, build-up, hold and drop off; generating hook load analysisusing at least one of the determined drilling activity and thedetermined wellbore conditions; and generating torque and drag analysisusing at least one of the determined drilling activity and thedetermined wellbore conditions.
 11. The system of claim 9, wherein thedetermining comprises executing a real-time annular hydraulics analysis,wherein the executing the real-time annular hydraulics analysiscomprises, in real-time: determining a velocity of a fluid based, atleast in part, on the non-real-time data inputs and the calibratedreal-time data inputs, wherein the determined velocity of the fluidcomprises a rate at which the fluid changes position over time within anannulus of the well; determining an effective viscosity of the fluidusing the determined velocity of the fluid; determining a ratio betweeninertial and viscous forces based, at least in part, on thenon-real-time data inputs and the calibrated real-time data inputs;determining an annular critical velocity and an annular critical flowrate using the determined ratio; determining a fanning friction factorusing the determined ratio based, at least in part, on the non-real-timedata inputs and the calibrated real-time data inputs; determining apressure loss gradient using the fanning friction factor, wherein thepressure loss gradient comprises the pressure lost across a unit lengthof measured depth; determining pressure loss due to friction using thedetermined pressure loss gradient; and determining an effective densitythat the fluid exerts against a formation in the well.
 12. The system ofclaim 11, wherein the executing the real-time annular hydraulicsanalysis comprises, in real-time: determining a sum of areas of at leastone jet through which the fluid travels based, at least in part, on thenon-real-time data inputs and the calibrated real-time data inputs;determining a rate at which the fluid is traveling through the at leastone jet using the determined sum of areas, wherein the determined rateat which the fluid is traveling through the at least one jet produces ajet velocity; determining a pressure loss as the fluid travels throughthe at least one jet; determining hydraulic power using the determinedpressure loss, wherein the hydraulic power is a measure of energy perunit time that is available to a drill bit as a result of the fluidtravelling through the at least one jet; and determining impact forceapplied to the formation using the jet velocity.
 13. The system of claim11, wherein the executing the real-time annular hydraulics analysiscomprises, in real-time: determining a boundary sheer rate based, atleast in part, on the non-real-time data inputs and the calibratedreal-time data inputs, wherein the boundary sheer rate is a measure ofvelocity change per unit distance experienced by the fluid at a wall ofthe well; determining a shear stress developed by a particle based, atleast in part, on the non-real-time data inputs and the calibratedreal-time data inputs, wherein the shear stress developed by theparticle is a measure of force applied by the particle on the fluid;determining a shear rate developed by the particle based, at least inpart, on the non-real-time data inputs and the calibrated real-time datainputs, wherein the shear rate developed by the particle is a measure ofvelocity change per unit distance experienced by the fluid as a resultof the particle; determining a slip velocity using at least one of thedetermined shear stress developed by the particle and the determinedshear rate developed by the particle, wherein the slip velocity is ameasure of rate at which the particle tends to fall towards a drill bit;determining a transport velocity using the determined slip velocity,wherein the transport velocity is a net rate at which the particletravels from the drill bit to a surface of the well; determiningtransport efficiency based, at least in part, on the non-real-time datainputs and the calibrated real-time data inputs, wherein the transportefficiency is a ratio of the determined transport velocity to thedetermined velocity of the fluid within the annulus of the well; anddetermining cutting concentration based, at least in part, on thenon-real-time data inputs and the calibrated real-time data inputs,wherein the cutting concentration is a ratio of the particles in theannulus of the well to a total annular volume of the well.
 14. Thesystem of claim 11, wherein the executing the real-time annularhydraulics analysis comprises, in real-time: determining an averagemaximum speed of pipe movement based, at least in part, on thenon-real-time data inputs and the calibrated real-time data inputs;determine an equivalent fluid velocity using the determined averagemaximum speed of pipe movement; determining an effective annularviscosity of the fluid using the determined equivalent fluid velocity;determining an annular ratio between inertial and viscous forces based,at least in part, on the non-real-time data inputs and the calibratedreal-time data inputs; determining an annular fanning friction factorusing the determined annular ratio based, at least in part, on thenon-real-time data inputs and the calibrated real-time data inputs;determining annular pressure loss gradient using the annular fanningfriction factor; determining at least one of swabbing friction loss andsurging friction loss using the determined annular pressure lossgradient; determining a gel-breaking pressure, wherein the gel-breakingpressure is a required force to push a pipe into a stationary fluid inthe well; and determining an equivalent fluid weight using at least oneof the gel-breaking pressure and the at least one of swabbing frictionloss and surging friction loss.
 15. A computer-program productcomprising a non-transitory computer-usable medium havingcomputer-readable program code embodied therein, the computer-readableprogram code adapted to be executed to implement a method comprising:receiving planned well-performance modeling data for a well currentlybeing drilled; receiving non-real-time data inputs in relation to thewell; receiving real-time data inputs produced by sensors in relation tothe well; receiving a correction factor that is indicative of drillingconditions; calibrating the real-time data inputs based, at least inpart, on the correction factor; determining well performance based, atleast in part, on the non-real-time data inputs and the calibratedreal-time data inputs; comparing, in real-time, the determined wellperformance with the planned well-performance modeling data for thewell; updating, in real-time, the planned well-performance modeling datafor the well based, at least in part, on the correction factor; andfacilitating a real-time display of comparison data for the well,wherein the real-time display comprises information related to thedetermined well performance and the updated planned well-performancemodeling data for the well.
 16. The computer-program product of claim15, wherein the determining comprises executing a real-time torque anddrag analysis, wherein the executing the real-time torque and draganalysis comprises, in real-time: determining drill string load for eachsection of a drill string based, at least in part, on the non-real-timedata inputs and the calibrated real-time data inputs; determiningdrilling activity based, at least in part, on the non-real-time datainputs and the calibrated real-time data inputs, wherein the drillingactivity comprises tripping in, rotating and tripping out; determiningwellbore conditions based, at least in part, on the non-real-time datainputs and the calibrated real-time data inputs, wherein the wellboreconditions comprises vertical, build-up, hold and drop off; generatinghook load analysis using at least one of the determined drillingactivity and the determined wellbore conditions; and generating torqueand drag analysis using at least one of the determined drilling activityand the determined wellbore conditions.
 17. The computer-program productof claim 15, wherein the determining comprises executing a real-timeannular hydraulics analysis, wherein the executing the real-time annularhydraulics analysis comprises, in real-time: determining a velocity of afluid based, at least in part, on the non-real-time data inputs and thecalibrated real-time data inputs, wherein the determined velocity of thefluid comprises a rate at which the fluid changes position over timewithin an annulus of the well; determining an effective viscosity of thefluid using the determined velocity of the fluid; determining a ratiobetween inertial and viscous forces based, at least in part, on thenon-real-time data inputs and the calibrated real-time data inputs;determining an annular critical velocity and an annular critical flowrate using the determined ratio; determining a fanning friction factorusing the determined ratio based, at least in part, on the non-real-timedata inputs and the calibrated real-time data inputs; determining apressure loss gradient using the fanning friction factor, wherein thepressure loss gradient comprises the pressure lost across a unit lengthof measured depth; determining pressure loss due to friction using thedetermined pressure loss gradient; and determining an effective densitythat the fluid exerts against a formation in the well.
 18. Thecomputer-program product of claim 17, wherein the executing thereal-time annular hydraulics analysis comprises, in real-time:determining a sum of areas of at least one jet through which the fluidtravels based, at least in part, on the non-real-time data inputs andthe calibrated real-time data inputs; determining a rate at which thefluid is traveling through the at least one jet using the determined sumof areas, wherein the determined rate at which the fluid is travelingthrough the at least one jet produces a jet velocity; determining apressure loss as the fluid travels through the at least one jet;determining hydraulic power using the determined pressure loss, whereinthe hydraulic power is a measure of energy per unit time that isavailable to a drill bit as a result of the fluid travelling through theat least one jet; and determining impact force applied to the formationusing the jet velocity.
 19. The computer-program product of claim 17,wherein the executing the real-time annular hydraulics analysiscomprises, in real-time: determining a boundary sheer rate based, atleast in part, on the non-real-time data inputs and the calibratedreal-time data inputs, wherein the boundary sheer rate is a measure ofvelocity change per unit distance experienced by the fluid at a wall ofthe well; determining a shear stress developed by a particle based, atleast in part, on the non-real-time data inputs and the calibratedreal-time data inputs, wherein the shear stress developed by theparticle is a measure of force applied by the particle on the fluid;determining a shear rate developed by the particle based, at least inpart, on the non-real-time data inputs and the calibrated real-time datainputs, wherein the shear rate developed by the particle is a measure ofvelocity change per unit distance experienced by the fluid as a resultof the particle; determining a slip velocity using at least one of thedetermined shear stress developed by the particle and the determinedshear rate developed by the particle, wherein the slip velocity is ameasure of rate at which the particle tends to fall towards a drill bit;determining a transport velocity using the determined slip velocity,wherein the transport velocity is a net rate at which the particletravels from the drill bit to a surface of the well; determiningtransport efficiency based, at least in part, on the non-real-time datainputs and the calibrated real-time data inputs, wherein the transportefficiency is a ratio of the determined transport velocity to thedetermined velocity of the fluid within the annulus of the well; anddetermining cutting concentration based, at least in part, on thenon-real-time data inputs and the calibrated real-time data inputs,wherein the cutting concentration is a ratio of the particles in theannulus of the well to a total annular volume of the well.
 20. Thecomputer-program product of claim 17, wherein the executing thereal-time annular hydraulics analysis comprises, in real-time:determining an average maximum speed of pipe movement based, at least inpart, on the non-real-time data inputs and the calibrated real-time datainputs; determine an equivalent fluid velocity using the determinedaverage maximum speed of pipe movement; determining an effective annularviscosity of the fluid using the determined equivalent fluid velocity;determining an annular ratio between inertial and viscous forces based,at least in part, on the non-real-time data inputs and the calibratedreal-time data inputs; determining an annular fanning friction factorusing the determined annular ratio based, at least in part, on thenon-real-time data inputs and the calibrated real-time data inputs;determining annular pressure loss gradient using the annular fanningfriction factor; determining at least one of swabbing friction loss andsurging friction loss using the determined annular pressure lossgradient; determining a gel-breaking pressure, wherein the gel-breakingpressure is a required force to push a pipe into a stationary fluid inthe well; and determining an equivalent fluid weight using at least oneof the gel-breaking pressure and the at least one of swabbing frictionloss and surging friction loss.